hugomimihu

There are 7 tiles, 2 of which are 1s.

so thus we have a 2/7 probability of drawing one for the first drawings, (2-1)/(7-1) = 1/6 for the second.

Multiplying the 2 gives 2/42 = 1/21.

Let's use casework for 2.

If he picks a 1, 2/7 probability, he then can choose 3 or 5, so 5/(7-1) = 5/6 probability. 10/42 = 5/21 probaility if he gets one first.

If he picks a 3, 3/7 probibiliity, he then can choose 5, so 2/(7-1) = 2/6= 1/3 probaility. The 3's cancel out so we have 1/7 probability.

If he picks 5 then we don't consider that, no larger.

We add the two probabilities and get 5/21 + 3/21 = 8/21.

If you don't understand anything feel free to ask.

The radius of the blue circle is 2+1 = 3 times the radius of the red, since the total diameter is 6r, divide 2 = 3.

πr^2 is the area of a red, divided by 2, and multiplied by 3 for the 3, so \(\frac{3πr^2}{2}\).

The radius of the blue is 3r, so (3r)^2 * π /2 is \(\frac{9πr^2}{2}\).

Since they are both divided by two, that is of little importance. They are all (number) times r^2 π, so r and π doesn't matter. The red is 3rπ, second is 9rπ, so  The ratio is 3:9 = 1:3, red:blue

If you don't understand anything feel free to ask!

Oh I get it now thanks for the explanation!!!

So a triangle's legs' sum must exceed the hypothenuse to be a triangle.

First, assuming c is positive, we have 1-2c and 1-c as the legs as they are each smaller than 1.

So,.

1-2c + 1-c >1

2-3c >1

1 >3c

1/3 >c

c < 1/3

That's after a bit of rearrangement.

NOW assuming c is 0. Hmm. That doesn't work since 1+1 = 2. Hmm.

NOW assuming that c is negative.

1-2c must be the hypothenuse as it is the largest, and 1 and 1-c are the legs.

1 + 1-c > 1-2c

2-c > 1-2c

1 > 2c

1/2 > c

c < 1/2

since c is smaller than 1/2 AND 1/3, we go with 1/3 since it's smaller than and the smallest.

c <1/3

If you don't understand anythign feel free to ask.

Which civilization are we talking about here???

We subtract the two volumes

π25*0.5 - π9*0.5 = 0.5π(25-9) = 0.5π * 16 = 8π.

That's 25.13 so 25.1

If you don't understand anything feel free to ask!  :)

Also it appears that the radius(based on image) is 4.5 since 4 and 5 seem to be equally above/below it.

In that case the diameter is 9.

Hmm.

My gut tells me that AD is 3*2 = 6...

So 2(3+3+4+5) = 2*15 = 30

Cphill probably meant AD is 2*4 

the formula for a cylinder's volume is π r^2 h =  (10/2)^2 π *3 = 75π.

that's about 235.619 m^3, or around 235619 liters. Subtracting the filled amount, we have 208084 liters.

If you don't understand anything feel free to ask!

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